For clarity, here is the condition in fraction notation:

$\frac{a}{b}=\frac{c}{d}$

This theorem says that the product of the left numerator and the right denominator is equal to the product of the left denominator and the right numerator.

In the proof, we first multiply both sides by b. Then we show that the left side reduces to a.

Next, we multiply both sides by d. At that point, the left side is:

a ⋅ d

Then we show that the right side reduces to

b ⋅ c

Quiz (1 point)

• a ⋅ b = b ⋅ a

• if a = b, then a ⋅ c = b ⋅ c

• if not (c = 0), then (b / c) ⋅ c = b

• if the following are true:

  • a = b
  • a = c

  then b = c

• if a = b, then a ⋅ c = b ⋅ c

• if not (b = 0), then ((a / b) ⋅ c) ⋅ b = a ⋅ c

• if the following are true:

  • a = b
  • b = c

  then a = c

• if the following are true:

  • a = b
  • b = c

  then a = c

Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.